IPO First-Day Return and Ex Ante Equity Premium

Hui Guo*

College of Business, University of Cincinnati

This Version: September 2009

* Contact: College of Business Administration, University of Cincinnati, Cincinnati, OH 45221; email address:

hui.guo@uc.edu; Tel: (513)556-7077; and Fax: (513) 556-0979. I thank an anonymous referee for extremely

constructive and insightful comments, which greatly improve the exposition of the paper. I thank Jay Ritter for

making IPO data and Amit Goyal for making predictive variables data available through their websites. I also thank

Paul Malatesta (editor), Robert Savickas, K.C. John Wei, Li Jin, Steve Slezak, Weihong Song, and conference

participants at the 2008 FMA meetings and the 2009 China International Conference in Finance for comments.

1

IPO First-Day Return and Ex Ante Equity Premium

Abstract

This paper proposes a measure of ex ante equity premium, IPOFDR, which is the average difference

between the IPO offer price and first-trading-day close price. I test the idea in three ways. First, there is a

positive relation between IPOFDR and future market returns. Second, changes in IPOFDR help explain

the cross-section of stock returns. Third, the predictive power of IPOFDR for stock returns reflects mainly

its close relation with market variance and average idiosyncratic variance—arguably measures of

systematic risk. These results cast doubt on the notion that the IPO first-day return is a measure of

investor sentiment.

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I. Introduction

Logue (1973), Ibbotson (1975), and others find that on average, the offer price at which the IPO

(initial public offering) shares are sold to investors is substantially lower than the price at which the

shares subsequently trade in the market. Numerous subsequent studies confirm that IPO underpricing is a

pervasive phenomenon in both U.S. and international financial markets. Most authors measure the

underpricing using the IPO first-day return—the percentage difference between the first-trading-day close

price and the offer price. For example, over the 1960 to 2006 period, the equal-weighted average U.S.

IPO first-day return is a stunning 17%1.

This paper investigates systematic movements of IPO underpricing and tests its implications for

asset pricing theories. In particular, I argue that the average IPO underpricing—defined as minus average

IPO first-day return and dubbed IPOFDR—is a proxy of ex ante stock market returns. Consistent with

this conjecture, I show that IPOFDR is closely related to measures of stock market risk and explains both

time-series and cross-sectional stock return predictability in a coherent manner. These novel empirical

findings provide support for a rational/risk-based interpretation of the information content of IPO

underpricing, while they cast doubt on the notion that the IPO first-day return is a measure of investor

sentiment (e.g., Baker and Wurgler (2006)).

I use two arguments to link IPOFDR to ex ante stock returns: (1) IPO underpricing mainly

reflects different discount rates used by issuers and investors and (2) issuers incorporate only partially

pricing information gathered during bookbuilding. Let us explain the first argument first. The present-

value relation proposed by Campbell and Shiller (1988) indicates that log stock prices equal expected

future log dividends minus expected future log discount rates. IPO underpricing thus reflects the fact that

relative to investors, issuers either (1) underestimate future cash flows or (2) overestimate future discount

rates. The first scenario is implausible for at least two reasons. First, holding back positive cash-flow

1 The calculation is based on the IPO first-day return data constructed by Jay Ritter, which are available through his

website: http://bear.cba.ufl.edu/ritter/ipodata.htm.

3

information is directly against issuers’ interest and has other undesirable side effects. For example, it

undermines investors’ confidence and thus may even jeopardize the outcome of IPOs. If issuers must

underprice IPO shares for a variety of reasons, they should use a higher discount rate instead. Second,

there is no good reason for investors to be more optimistic about cash flows than issuers, especially

because issuers—who are likely to be better informed—have incentives to exaggerate their fundamentals.

The expected value of IPOFDR is approximately constant if issuers give investors a constant

discount that is invariant to business conditions. Thus, the second assumption—partial adjustment of offer

prices to pricing information gathered during bookbuilding—plays a crucial role in establishing the link

between IPOFDR and ex ante equity premium. The assumption is motivated by the well-documented

empirical evidence, e.g., Hanley (1993). It is also a key implication of several leading explanations of IPO

underpricing (e.g., Benveniste and Spindt (1989), Loughran and Ritter (2002), and Edelen and Kadlec

(2005)). I show that because of partial adjustment, IPOFDR is mechanically related to investors’ expected

market returns. Many empirical studies also find that the adjustment of offer prices is more complete in

cold markets than in hot markets. This stylized fact implies a stronger link between IPOFDR and ex ante

equity premium in hot markets than in cold markets. Assuming that investors price IPOs rationally, I test

these refutable implications in three ways using U.S. data over the 1960 to 2006 period.

First, as hypothesized, there is a positive and statistically significant relation between IPOFDR

and future excess market reruns in both in-sample and out-of-sample tests, and the relation is stronger for

IPOFDR in hot markets than for IPOFDR in cold markets. Second, if IPOFDR is a proxy of expected

discount rates, Merton (1973) and Campbell’s (1993) intertemporal capital asset pricing models (ICAPM)

suggest that it should help explain the cross-section of expected stock returns. Consistent with this

implication, the (unanticipated) change in IPOFDR is closely correlated with the value premium factor

(HML) of the Fama and French (1996) three-factor model, for which Fama and French and many others

advocate an intertemporal pricing interpretation. More importantly, the variables IPOFDR and HML have

similar explanatory power for the cross-section of returns on twenty-five Fama and French portfolios

sorted by size and book-to-market equity ratio. Lastly, in ICAPM, conditional equity premium is

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determined by the conditional variances of market returns and hedging factor(s); and Guo and Savickas

(2008) argue that average idiosyncratic stock variance is a proxy for the latter. Consistent with the

ICAPM implication, I find that IPOFDR correlates positively with market variance and negatively with

average idiosyncratic variance. More importantly, the predictive power of IPOFDR for market returns

comes mainly from its close correlation with the two variances.

A direct measure of ex ante equity premium has important implications for empirical asset pricing

research. For example, by contrast with the existent empirical studies but consistent with the present-

value relation, I uncover a negative relation between the dividend yield and future dividend growth after

controlling for the effect of IPOFDR on future dividend growth, which is found to be significantly

positive. The latter result, which suggests a positive relation between expected equity premium and

expected dividend growth, is consistent with the finding by Lettau and Ludvigson (2005).

The empirical findings in this paper are consistent with the general equilibrium model of optimal

IPO timing proposed by Pastor and Veronesi (2005), who argue that investors price IPOs rationally and

that time-varying discount rates have significant effects on the market valuation of IPOs.2 Their model

predicts a negative relation between IPO volumes and expected discount rates, as observed in data.

Because the average IPO first-day return and the number of IPOs are positively correlated (e.g., Lowry

(2003)), Pastor and Veronesi’s model helps understand the strong empirical link between IPOFDR and ex

ante equity premium, as documented in this paper. For example, Baker and Wurgler (2000) find that the

equity share in new issues forecasts stock market returns. I find that the predictive power of the equity

share is related to that of IPOFDR—it becomes statistically insignificant after controlling for IPOFDR in

the forecasting regression. This finding casts doubt on Baker and Wurgler’s interpretation that investors

price IPOs irrationally and managers issue more new equities when stocks are overvalued.

2 Zhang (2005) and Carlson, Fisher, and Giammarino (2006) investigate theoretically the effect of time-varying

discount rates on the price of new equity issues using equilibrium models.

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Baker and Wurgler (2006) construct an index using six commonly used measures of investor

sentiment, including the equity share of new issues and the IPO first-day return. They show that expected

returns on stocks that have highly subjective valuation and high arbitrage costs—e.g., small young growth

stocks—behave differently across high and low sentiment states. Interestingly, I find that the investor

sentiment index and its components are closely correlated with measures of systematic risk, i.e., market

variance and average idiosyncratic variance. Moreover, ICAPM accounts for the conditional relation

between investor sentiment and the cross-section of stock returns in a coherent manner. Overall, the

empirical results suggest that mispricing is unlikely to be a main driver of stock market fluctuation.

Pastor, Sinha, and Swaminathan (2008) construct a measure of ex ante equity premium using

implied costs of capital. These authors mainly focus on the stock market risk-return relation and do not

investigate whether their measure forecasts stock market returns or explains the cross-section of stock

returns. Moreover, while Pastor, Sinha, and Swaminathan find a positive relation between conditional

market return and variance, the simple relation between IPOFDR and conditional market variance is

found to be rather weak in this paper. Nevertheless, I am able to uncover a significantly positive risk-

return tradeoff after controlling for the hedging risk factor.

The remainder of this paper proceeds as follows. I derive the theoretical relation between the IPO

first-day return and expected future discount rates in Section II. I explain data in Section III. I present the

main empirical results in Section IV. I compare the rational versus irrational interpretations of IPOFDR’s

information content in Section V. I offer some concluding remarks in Section VI.

II. IPO First-Day Return and Expected Future Discount Rates

Most of existent studies advocate for a rational pricing interpretation of IPO underpricing with

three noticeable exceptions—information cascade by Welch (1992), investor sentiment by Ljungqvist,

Nanda, and Singh (2004), and agency conflicts between issuers and underwriters by Loughran and Ritter

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(2002).3 Because they suggest that investors price IPO irrationally, the first two models do not explain

this paper’s main finding that IPO first-day return is a proxy of ex ante equity premium. Loughran and

Ritter (2002) argue that (rational) underwriters deliberately lower the offer price of IPO shares in

exchange for favors from institutional investors to whom offerings are allocated. By contrast, (irrational)

issuers are not upset by substantial amounts of money left on the table because of mental accounting. The

finding that information content of IPO underpricing reflects rational pricing is potentially consistent with

Loughran and Ritter’s model, in which underwriters set the offer price and investors price IPOs rationally.

With this caveat in mind, for simplicity, in this section I assume that issuers, underwriters, and investors

are rational and that there are no agency conflicts between issuers and underwriters.

If investors price IPO shares rationally, the market price of IPO shares equals the expected

discounted future dividends. Using the present value relation, Campbell and Shiller (1988) show that the

log market price equals approximately the expected future log dividends minus the expected future log

discount rates

(1) , , 1 , 10

( ) [ {(1 ) }]1

ji t i t i t j i t j

j

kP E d rρ ρρ

∞

+ + + +=

= + − −− ∑ ,

where ( )1 i

kρ−

is a constant, tE is the expectation operator based on investors’ information set, , 1i t jd + + is

the log dividend, and , 1i t jr + + is the log equilibrium discount rate. Campbell and Shiller’s loglinearization

can also be applied to the offer price ( ,O

i tP ) of IPO shares

(2) , , 1 , 10

( ) [ {(1 ) }]1

O O O j Oi t i t i t j i t j

j

kP E d rρ ρρ

∞

+ + + +=

= + − −− ∑ ,

3 Ritter and Welch (2002), Ritter (2003), and Ljungqvist (2004) provide comprehensive surveys of both empirical

evidence and theoretical explanations of IPO underpricing.

7

where ( )1

Oi

kρ−

is a constant, OtE is the expectation operator based on issuers’ information set, and

, 1O

i t jr + + is the log discount rate adopted by issuers.

Unlike the market price of IPO shares, the offer price is not directly determined by the market

equilibrium condition of supply and demand.4 We thus can think of , 1O

i t jr + + as an implied discount rate

that equates the offer price with expected cash flows in equation (2). In particular, as I explain below, if

issuers need to underprice IPO shares for some reasons, e.g., asymmetric information or legal

considerations, they do so by using a discount rate, , 1O

i t jr + + , that is higher than the equilibrium discount

rate, , 1i t jr + + . In other words, the difference between issuers and investors’ discount rates captures various

theoretical explanations of IPO underpricing.

By definition, the IPO first-day return is the difference between ,i tP and ,O

i tP :

(3) , , , , 1

0

, 1 , 10 0

( )[ (1 ) ]

[ ( ) ( )]

O O ji t i t i t i t t i t j

j

j O j Ot i t j t i t j

j j

r P P c E E d

E r E r

ρ ρ

ρ ρ

∞

+ +=

∞ ∞

+ + + += =

= − = + − −

+ − − −

∑

∑ ∑,

where ( ) ( )1 1

Oi i i

k kcρ ρ

= −− −

is a constant. Ignoring the constant term because it does not contribute to

time-series variation in IPO underpricing, equation (3) shows that the IPO first-day return is positive

under two conditions. First, investors are more optimistic about the firm’s cash flows than are issuers.

Second, investors require lower expected discount rates than do issuers. That is, in equation (3) I

decompose IPO underpricing into underpricing of fundamentals and underpricing of discount rates.

Existing economic theories of IPO underpricing—e.g., asymmetric information, institution explanations,

ownership and control, and behavioral explanations—do not explicitly make such a distinction between

4 Ritter and Welch ((2002), p.1803) argue that “Thus, the solution to the underpricing puzzle has to lie in focusing

on the setting of the offer price, where the normal interplay of supply and demand is suppressed by the underwriter.”

8

fundamentals and discount rates, however. I argue below that underpricing of fundamentals is unlikely an

important driver of the positive IPO first-day return for at least two reasons.

First, issuers have no incentive to underestimate their fundamentals because doing so will lower

the offer price that they receive from investors. More importantly, because issuers need to disclose their

expected cash flows in the prospectus, understating fundamentals will undermine investors’ confidence

and thus may even jeopardize the outcome of IPOs. If issuers must underprice their IPO shares for various

reasons mentioned above, they can raise the discount rate in equation (2) instead of reporting understated

cash flows in the prospectus. To summarize, because of undesirable side effects associated with

understating fundamentals, it is optimal for issuers to adjust the offer price through the discount rate.

Second, if investors are rational, there are no apparent reasons why they should be more

enthusiastic about cash flows than issuers. In particular, given that issuers have incentives to exaggerate

fundamentals because of superior information about their own firms, doing so will likely cost investors

more money to purchase IPO shares. Some authors, e.g., Ljungqvist, Nanda, and Singh (2006), argue that

investors are sometimes overoptimistic about the prospective of IPO firms and investor sentiment may

temporarily drive up the market price of IPO shares above the fair value.5 By contrast with this

interpretation, I find that commonly used measures of investor sentiment, including IPOFDR, are closely

correlated with the determinants of ex ante equity premium, however.

Of course, I am not suggesting that investors and issuers have the same expectation about

fundamentals or , 10

( )[ (1 ) ] 0O jt t i t j

j

E E dρ ρ∞

+ +=

− − =∑ . Rather, if both investors and issuers are rational, the

difference of their expectations is likely to be idiosyncratic and can be averaged away if tN —the number

of IPOs during period t—is large:

5 Ljungqvist, Nanda, and Singh (2006) argue that their model explains the long-run underperformance of IPO stocks,

as documented by Ritter (1991) and others. Lyandres, Sun, and Zhang (2008), however, show that Ritter’s result

may reflect time-varying risk premium.

9

(4) , 10

1 ( )[ (1 ) ] 0tN

O jt t i t j

i jt

E E dN

ρ ρ∞

+ +=

− − ≈∑ ∑ .

That is, substantial amounts of money left on the table should not be a surprise to issuers; rather, they are

the consequence of issuers’ own actions, e.g., using a high discount rate. Otherwise, subsequent issuers

will rationally bargain hard for a better offer price. This assumption is consistent with Ritter and Welch’s

((2002), p.1802) argument that “simple fundamental misvaluation or asset pricing risk premia are unlikely

to explain the average first-day return of 18.8%. ”

Hanley (1993) finds that issuers adjust the final offer price only partially to favorable pricing

information gathered during bookbuilding. Her finding is confirmed by numerous subsequent studies

using both U.S. and international data. This so-called “partial adjustment” phenomenon is also an

important feature of several leading explanations of IPO underpricing. In particular, Benveniste and

Spindt (1989) argue that it is a form of compensation to investors for revealing their favorable private

information. Alternatively, Loughran and Ritter (2002) propose that partial adjustment is mainly driven

by agency conflicts between issuers and underwriters, while Edelen and Kadlec (2004) suggest that it

reflects the fact that issuers trade off the proceeds from the IPO against the probability of the IPO

succeeding. If underpricing of fundamentals is unlikely an important source of the positive IPO first-day

return, as I argued above, partial adjustment of the offer price implies that issuers adjust their discount

rates only partially to their expected investors’ discount rates, , 10

( )O jt i t j

j

E rρ∞

+ +=

−∑ :

(5) , 1 , 10 0

( ) ( )O j O O jt i t j it t i t j it

j j

E r E rρ α ρ μ∞ ∞

+ + + += =

− = − −∑ ∑ ,

where the coefficient, itα , is less than one.6 Some other theoretical explanations of IPO underpricing—

e.g., asymmetric information among investors by Rock (1986) and legal considerations by Tinic (1988) 6 Hanley (1993) and many other authors interpret partial adjustment as empirical support for Benveniste and

Spindt’s (1989) bookbuilding theory. Ritter and Welch (2002), however, are skeptical about this view by arguing

that equilibrium compensation for revealing favorable information accounts for only a small fraction of the observed

10

and Lowry and Shu (2002)—do not involve partial adjustment of the offer price, however. I use the term

itμ in equation (5) to capture the effect of these factors on IPO underpricing, and assume that it is

approximately stable across time

(6) 1 ( )tN

ititN

μ μ− ≈−∑ .

Therefore, while partial adjustment is a crucial assumption for the link between the IPO first-day return

and ex ante equity premium, it is not the only explanation of IPO underpricing.

Using equation (5), I can write the underpricing of discount rats as

(7) , 1 , 1

0 0

, 1 , 10 0

( ) ( )

(1 ) [ ( )] ( )[ ( )]

j O j Ot i t j t i t j

j j

j O jit t i t j it t t i t j it

j j

E r E r

E r E E r

ρ ρ

α ρ α ρ μ

∞ ∞

+ + + += =

∞ ∞

+ + + += =

− − − =

− − + − − +

∑ ∑

∑ ∑.

Again, if both investors and issuers are rational, The difference of their expectations about future

investors’ discount rates, , 10

( )[ ( )]O jt t i t j

j

E E rρ∞

+ +=

− −∑ , is an idiosyncratic random shock with zero mean.

Because there is no compelling reason that , 10

( )[ ( )]O jt t i t j

j

E E rρ∞

+ +=

− −∑ and itα should be correlated, their

product is also a random variable with zero mean when tN is large:

(8) , 10

1 ( )[ ( )] 0tN

O jit t t i t j

i jt

E E rN

α ρ∞

+ +=

− − ≈∑ ∑ .

Using equations (3) to (8), the average IPO underpricing is

IPO underpricing. Moreover, Loughran and Ritter (2002) and Bradley and Jordan (2002) find that issuers do not

incorporate fully public information in the form of pre-pricing returns on the market index. This finding casts doubt

on Benveniste and Spindt’ interpretation, while it is consistent with the models by Loughran and Ritter (2002) and

Edelen and Kadlec (2004). Lowry and Schwert (2004), however, argue that partial adjustment to public information

is economically unimportant. A formal test of these alternative hypotheses of partial adjustment is beyond the scope

of this paper, and I simply interpret equation (5) as a reduced form that is motivated by empirical evidence.

11

(9) , , 11 1 0

1 1 [(1 ) ( )]t tN N

ji t it t i t j

i i jt t

r c E rN N

μ α ρ∞

+ += = =

≈ + + − −∑ ∑ ∑ ,

where 1

1 tN

iit

c cN =

= ∑ is a constant. I further assume that

(10) it t itα α η= + ,

where tα is the systematic component of the degree of the adjustment in the offer price and itη is the

idiosyncratic component. For example, on average, itα is small (large) during hot (cold) markets because

tα is small (large). The effect of itη on the offer price can be averaged away across a large number of

IPOs even though it is potentially important for an individual IPO:

(11) , 11 0

1 0tN

jit t i t j

i jt

E rN

η ρ∞

+ += =

=∑ ∑ .

Substituting equations (10) and (11) into equation (9), I obtain

(12) , , 11 1 0

1 1(1 ) [ ( )]t tN N

ji t t t i t j

i i jt t

r c E rN N

μ α ρ∞

+ += = =

≈ + + − −∑ ∑ ∑ .

Note that if tN is relatively large, the cross-sectional average of expected discount rates is

approximately equal to expected market returns:

(13) , 1 , 1 , 11 0 0 1 0

1 1( ) [ ]t tN N

j j jt i t j t i t j t m t j

i j j i jt t

E r E r E rN N

ρ ρ ρ∞ ∞ ∞

+ + + + + += = = = =

= ≈∑ ∑ ∑ ∑ ∑ .

Given that firms going public tend to be young small growth firms, the cross-sectional average of IPO

firms’ discount rates is unlikely to be representative of market returns. Nevertheless, I still expect a strong

correlation between the two variables because the valuation of young small growth stocks is very

sensitive to changes in aggregate discount rates (e.g., Campbell and Vuolteenaho (2004)).7 With this

caveat in mind, I substitute equation (13) into equation (12) and obtain

7 Campbell and Vuolteenaho (2004) use this argument to motivate the use of small stock value spread as a predictive

variable of market returns in the estimation of ICAPM.

12

(14) , , 11 0

1 (1 )tN

ji t t t m t j

i jt

r c E rN

μ α ρ∞

+ += =

≈ + − −∑ ∑ .

Because partial adjustment implies that the coefficient iα is less than one, Equation (14) shows that the

average IPO first-day return is negatively related to the expected future market returns. For example, if

the average IPO first-day return is high in the current year, one would expect a fall in market indices in

the following year. To provide a direct measure of expected market returns, I define the variable IPOFDR

as minus average IPO first-day return:

(15) , , 11 0

1IPOFDR (1 ) , 0< 1tN

jt i t t t m t j t

i jt

r E r cN

α ρ μ α∞

+ += =

=− ≈ − − − <∑ ∑ .

In the empirical analysis, I test three refutable implications of Equation (15). First, IPOFDR

forecasts the excess stock market return, ERET:

(16) 1 1ERET * IPOFDRt t tθ γ ε+ += + + .

In particular, IPOFDR is positively related to future stock market returns or the coefficient γ is positive.

Moreover, because tα is smaller in hot markets than in cold markets, the coefficient γ should be larger

for IPOFDR in hot markets than for IPOFDR in cold markets. Second, Merton (1973) and Campbell’s

(1993) ICAPM implies that innovations in IPOFDR are a priced risk factor and help explain the cross-

section of stock returns. Third, IPOFDR should correlate with measures of systematic risk that affect

conditional equity premium. I present the empirical tests of these refutable implications in Section IV

after I briefly discuss data next.

III. Data

I obtain data of monthly equal-weighted IPO first-day return and monthly number of IPOs over

the period January 1960 to December 2006 from Jay Ritter at the University of Florida. In the empirical

analysis, I convert monthly data into annual data for three reasons. First, there are no IPOs for several

consecutive months, e.g., July 1974 to December 1974. There is a missing observation problem if using

13

monthly or quarterly data. Second, Section II shows that IPOFDR is a proxy of expected market returns if

it is the average of a large number of IPOs. Using annual data allows us to obtain a reliable measure of

expected market returns. Third, because IPOFDR is the sum of discounted future returns over infinite

horizons, it may have stronger forecasting ability for stock returns over long (e.g., annual) horizons than

over short (e.g., monthly or quarterly) horizons. Nevertheless, I find that main results are qualitatively

similar for semi-annual and quarterly data.

[Insert Figure 1 here]

Figure 1 plots the standardized annual IPOFDR (solid line) and the annual number of IPOs over

the period 1960 to 2006. The variable IPOFDR exhibits two noteworthy patterns that are consistent with

the conjecture that it is a proxy of ex ante equity premium. First, IPOFDR tends to increase sharply just

before or during business recessions dated by the National Bureau of Economic Research (NBER), as

indicated by shaded areas. The pattern is consistent with the conventional wisdom (e.g., Fama and French

(1989) and Campbell and Cochrane (1999)) that conditional equity premium moves countercyclically

across time. Second, as observed by Loughran and Ritter (2002), IPOFDR appears to have strong serial

correlation. The pattern is consistent with the notion that conditional equity premium is persistent.

I use annual value-weighted S&P 500 index return obtained from Standard and Poor’s as a

measure of market returns, and results are qualitatively similar if using CRSP (Center for Research in

Security Prices) annual value-weighted market returns. The risk-free rate is obtained from CRSP. I obtain

from Kenneth French at Dartmouth College the annual Fama and French (1996) three factors and the

annual returns on twenty-five Fama and French portfolios sorted on size and book-to-market equity ratio.

I obtain quarterly dividends per share from Standard and Poor’s. Consumer price index (CPI) is

used to convert nominal dividends into real dividends, and annual real dividends are the sum of quarterly

real dividends in a year. As s robustness check, following Fama and French (1988), I use CRSP monthly

total return index and price index to back out monthly dividends per share and then sum them up to obtain

annual dividends. The results are qualitatively similar to those using Standard and Poor’s dividends; for

brevity, they are not reported here. Results are, however, different if I back out annual dividends using

14

CRSP annual total return index and annual price index, as in Lettau and Ludvigson (2005). In particular,

because dividends are reinvested and compounded in the construction of CRSP annual total return index,

the dividend growth based on annual indices is much more volatile and has substantially stronger

correlation with market returns than the dividend growth calculated using monthly indices. I will return to

this point when discussing the empirical evidence of forecasting dividend growth in Section IV.

[Insert Table 1 here]

Table 1 provides summary statistics of some selected variables. Consistent with the visual

inspection of Figure 1, IPOFDR is serially correlated, with an autocorrelation coefficient of 44%. Its first

difference, IPOFDRΔ , is serially uncorrelated, however. IPOFDR is negatively correlated with the

excess market return, ERET, with a correlation coefficient of –16%. This result is consistent with the

conventional wisdom that IPO underpricing is larger when market conditions are good than when market

conditions are bad. Interestingly, there is an even stronger negative relation between IPOFDRΔ and

ERET: The correlation coefficient is –48%. This new stylized fact is consistent with the conjecture that

IPOFDR is a proxy of expected equity premium: French, Schwert, and Stambaugh (1987), Guo and

Whitelaw (2006), and others emphasize that an unexpected increase in discount rates leads to a

contemporaneous fall in stock market indices.

Table 1 also reveals a strong positive relation between IPOFDRΔ and the HML factor of the

Fama and French (1996) three-factor model, with the correlation coefficient of about 49%. HML is the

return difference between value and growth stocks. Because Campbell and Vuolteenaho (2004) find that

prices of growth stocks are more sensitive to variation in discount rates than are prices of value stocks,

HML is arguably a proxy of discount-rate shocks. Therefore, the strong positive relation between

IPOFDRΔ and HML should be expected if, as I explained in Section II, IPOFDR is a proxy of ex ante

equity premium.

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IV. Empirical Results

A. Explaining Time-Series Variation in IPOFDR

Most of leading intertemporal asset pricing theories, e.g., Merton (1973), Campbell (1993),

Campbell and Cochrane (1999), and Bansal and Yaron (2004), suggest that ceteris paribus, conditional

stock market variance should be positively correlated with conditional excess stock market returns.8

Following Merton (1980) and Andersen, Bollerslev, Diebold, and Labys (2003), I measure conditional

stock market variance using realized stock market variance, MV, which is the sum of squared daily excess

stock market returns in a given period. If IPOFDR is a proxy of expected stock market returns, its

correlation with MV should be positive. This implication is essentially a test of the positive risk-return

relation in the stock market using an ex ante measure of equity premium, as advocated by Pastor, Sinha,

and Swaminathan (2008), although their measure is different from the one used in this paper.

Panel A of Table 2 reports the OLS estimation results of regressing IPOFDR on a constant and

MV. Over the period 1960 to 2005, the relation is positive but statistically insignificant; and the adjusted

R2 is even negative. Overall, MV accounts for little variation in ex ante equity premium. The results are

qualitatively similar for three subsamples (1960 to 1982, 1982 to 2005, and 1960 to 1995)—the effect of

market variance on conditional equity premium is positive but statistically insignificant at conventional

levels. As a robustness check, I repeat the above analysis using first differences instead of levels. That is,

if there is a positive risk-return tradeoff, an increase in conditional market variance will raise ex ante

equity premium that investors require for holding a market index. Panel B shows that the main results are

8 Campbell and Cochrane (1999) do not provide an analytical solution for the relation between conditional equity

premium and conditional variance for their habit-formation model. Simulated data from their model show a stable

relation between the two variables, however. The result reflects the fact that because there is only one state

variable—i.e., the consumption surplus ratio—in the habit-formation model, conditional equity premium,

conditional variance, and the dividend yield move closely to each other.

16

qualitatively similar to those obtained using levels—the risk-return relation is statistically insignificant at

conventional levels.

[Insert Table 2 here]

To summarize, consistent with the finding by many early authors, e.g., Campbell (1987), French,

Schwert, and Stambaugh (1987), Glosten, Jagannathan, and Runkle (1993), and Whitelaw (1994), there is

little empirical support for a positive risk-return tradeoff in the stock market. The evidence, however, is

different from that obtained by Pastor, Sinha, and Swaminathan (2008), who use the implied cost of

capital as a measure of ex ante equity premium and find that it is positively and significantly related to

conditional market variance. Because ex ante equity premium is not directly observable, the difference

reflects measurement errors in its proxies. Before providing more stringent tests on the hypothesis that

IPOFDR is a proxy of ex ante equity premium, I first try to explain why the simple relation between

IPOFDR and conditional market variance is rather weak.

Failing to uncover a positive risk-return relation in the stock market may reflect an omitted

variable problem. Scruggs (1998) and Guo and Whitelaw (2006) argue that ignoring the effect of the

hedge component on expected excess stock market returns leads to a downward bias in the estimated risk-

return relation. For example, Guo and Whitelaw uncover a positive and statistically significant risk-return

tradeoff after controlling for the consumption-wealth ratio (CAY) proposed by Lettau and Ludvigson

(2001) as a proxy for the hedge component. Moreover, Guo and Savickas (2008) argue that average

idiosyncratic variance (IV) is a measure of investment opportunities and find that it is closely correlated

with CAY and that the two variables have similar forecasting power for stock market returns.9 Because

CAY is estimated using full sample and thus may potentially have a look-ahead bias, in this paper I

9 Cao, Simin, and Zhao (2008) provide empirical evidence that average idiosyncratic variance moves closely with

standard measures of investment opportunities.

17

follow Guo and Savickas in the construction of the variable IV and use it as a proxy for the hedge

component.10 Figure 2 plots IV and MV over the period 1960 to 2005.

[Insert Figure 2 here]

I reinvestigate the risk-return relation using IV as a proxy for the hedge component of expected

equity premium. Panel C of Table 2 reports the multivariate OLS estimation results of regressing

IPOFDR on a constant, MV, and IV. Interestingly, as hypothesized, after controlling for IV, the positive

relation between MV and IPOFDR becomes statistically significant at the 1% level in the full sample

period 1960 to 2005. Consistent with Guo and Savickas (2008), the relation between IV and expected

market returns (as measured by IPOFDR) is negative and statistically significant at the 1% level.

Moreover, the adjusted R2 increases sharply to over 30%, indicating that MV and IV jointly account for a

significant portion of variation in IPOFDR. The results are qualitatively similar in three subsamples.

Panel D of Table 2 shows that using the first difference in the regression produces qualitatively similar

results as well. To summarize, I uncover a significantly positive relation between IPOFDR and MV after

controlling for the effect of IV on conditional equity premium.

The difference between panels A and C of Table 2 reflects an omitted variable problem. Note that

the effects of MV and IV on IPOFDR have opposite signs (panel C of Table 2), although the two

variables are positively correlated with each other (Figure 2). Therefore, omitting the hedge component

(as approximated by IV) introduces a downward bias in the slope coefficient of the regression reported in

panel A. These results are also consistent with those reported by Guo and Savickas (2008), who find that

MV is positively correlated with future stock market returns, while the relation is negative for IV. To

summarize, IPOFDR correlates significantly with IV and MV with expected signs. This result is

consistent with the conjecture that IPOFDR is a proxy of ex ante market returns.

10 Scruggs (1998) use returns on long-term government bonds as a measure of investment opportunities. In a

subsequent study, Scruggs and Glabadanidis (2003) find that the result is sensitive to the assumption that the

correlation coefficient between stock and bond returns are constant across time.

18

B. Forecasting One-Year-Ahead Excess Stock Market Returns

If IPOFDR is a measure of ex ante equity premium, it should forecast stock market returns. To

address this issue, panel A of Table 3 reports the OLS estimation results of forecasting one-year-ahead

excess stock market returns using IPOFDR. Over the full sample 1961 to 2006, IPOFDR is positively

related to future market returns and the relation between the two variables is statistically significant at the

1% level. The adjusted R2 is about 11%, indicating that IPOFDR accounts for a sizable portion of

variation in market returns. In Figure 3, I plot IPOFDR along with one-year-ahead excess stock market

returns. It shows that the two variables tend to move in the same direction and the result does not appear

to be driven by influential observations.

[Insert Table 3 here]

[Insert Figure 3 here]

Panel A of Table 3 also shows that I obtain qualitatively similar results for three subsamples. For

example, the relation between IPOFDR and future excess stock market returns is always positive in the

two half samples (1961 to 1982 and 1983 to 2006) as well as in the subsample ending in 1995. However,

while the relation is statistically significant at the 1% level in the second half sample, it is insignificant at

the 10% level in the first half sample. Arguably the difference may be partially attributed to the lack of

power because of relatively small number of annual observations used in the subsamples. For example,

the relation becomes marginally significant over the period 1961 to 1995. Below I discuss two other

possible explanations: (1) The relation between IPOFDR and expected returns changes across business

cycles and (2) the estimation is biased because IPOFDR is a noisy measure of ex ante equity premium.

First, recall that in equation (15), tα is larger in cold markets than in hot markets because the

offer price adjusts to market information more completely in cold markets than in hot markets. Figure 1

shows that business conditions are noticeably weaker in the first half sample than in the second half

sample. For example, there are four recessions in the first half sample but there are only two recessions in

the second half sample. More important, if the number of IPOs is an indicator of cold or hot markets (e.g.,

19

Pastor and Veronesi (2005)), IPO markets are substantially colder in the first half sample than the second

half sample. These facts help explain the evidence that the relation between IPOFDR and future stock

returns is weaker in the first half sample than in the second half sample, as reported in panel A of Table 3.

To investigate formally this issue, I construct a dummy variable, DUM, which equals one for the years

during which the number of IPOs is less than 200 and equals zero otherwise. Panel B of Table 3 reports

the OLS estimation results of the regression with the dummy variable for cold markets:

(17) 1 1ERET IPOFDR IPOFDR * DUMt t t t tθ γ δ η+ += + + + .

In equation (17), I expect that the coefficient δ is negative or that the effect of IPOFDR on future stock

returns is weaker in cold markets than in hot markets.

Panel B of Table 3 shows that, as expected, the point estimate of δ is significantly negative in

the first half sample 1961 to 1983 as well as in the subsample 1961 to 1995. Interestingly, the coefficient

γ , which measures the total effect of IPOFDR on future stock returns, is now positive and statistically

significant at the 5% level in both subsamples. Because of few years of cold markets, the coefficient δ is

imprecisely estimated for the second half sample 1984 to 2006, however. Overall, in the full sample 1961

to 2006, the coefficient δ is negative but statistically insignificant. Note that the total effect of IPOFDR

in cold markets on expected stock returns, γ δ+ , is always positive, indicating that there is also partial

adjustment in the offer price during cold markets. To summarize, the results confirm the finding by

Hanley (1993) and others that issuers incorporate only partially market information in their offer prices.

Second, as explained in Section II, IPOFDR is only a proxy of expected stock returns and have

measurement errors. To address this issue, I repeat the above analysis using the two-stage least squares

(2SLS). I use IV and MV as the instrumental variables because their predictive power for market returns

is similar to that of IPOFDR. (The result is omitted for brevity) In the 2SLS regressions, the relation

between IPOFDR and future market returns is always statistically significant at the 1% level. Moreover,

the point estimates from the 2SLS regressions are substantially larger than their OLS counterparts

reported in Table 3 due to the attenuation effect of measurement errors.

20

As a robustness check, I investigate whether IPOFDR has significant predictive power after

controlling for the forecasting variables considered in Goyal and Welch (2008). Over the period 1961 to

2006, I find that the effect of IPOFDR always remains significantly positive except when combined with

CAY. Lettau and Ludvigson (2001) argue that CAY forecasts stock returns because of its close relation

with expected future market returns; therefore, the evidence is again consistent with the conjecture that

IPOFDR is a proxy of ex ante equity premium. Similarly, except for CAY, the other variables, however,

have negligible predictive ability for stock returns after controlling for IPOFDR. For brevity, I do not

report these results here but they are available on request. To summarize, the main result in this paper

differs from that of Goyal and Welch because IPOFDR provides additional information about future stock

returns beyond the variables that these authors consider.

C. Out-of-Sample Forecast

[Insert Table 4 here]

In this subsection, I compare the out-of-sample forecasts of the proposed forecasting variable

(IPOFDR) with a benchmark model of constant expected market returns. I use three test statistics to

gauge the relative performance—the mean-squared error (MSE) ratio; the encompassing test (ENC-

NEW) proposed by Clark and McCracken (2001); and the equal forecast accuracy test (MSE-F) proposed

by McCracken (1999). As in Lettau and Ludvigson (2001), I use the first one-third of the sample (1961 to

1977) for the initial in-sample regression and then make out-of-sample forecasts for the remainder of the

sample recursively. For ENC-NEW and MSE-F tests, I report the bootstrap 5% critical values.

The first row of Table 4 reports the results for IPOFDR. The MSE ratio between the forecasting

model and the benchmark model is 0.85, suggesting that on average the forecasting model has

substantially smaller squared forecasting errors than does the benchmark model. Similarly, the ENC-

NEW test statistic is 4.22, which is substantially larger than the 5% bootstrap critical value of 2.50. Thus,

the difference between the forecasting model and the benchmark model is statistically significant. I obtain

the same conclusion using the MSE-F test. I also include the dummy variable for cold markets, and the

21

second row of Table 4 shows that results are qualitatively similar to those reported in the first row. To

summarize, IPOFDR has significant out-of-sample forecasting ability for excess market returns.

D. IPOFDR and the Cross-Section of Stock Returns

If IPOFDR is a proxy of expected discount rates, ICAPM indicates that innovations in IPOFDR

are a priced risk factor and help explain the cross-section of stock returns. Because the first difference,

IPOFDR , is serially uncorrelated (Table 1), it can be used as a proxy for innovations in IPOFDR. To be

robust, I show that using alternative measures of innovations generates qualitatively similar results.

Recent authors, e.g., Campbell and Vuolteenaho (2004), Petkova (2006), and Hahn and Lee

(2006), find that HML is a priced risk factor because of its close relation with the discount-rate shock. In

particular, Campbell and Vuolteenaho (2004) find that growth stocks are more sensitive to the discount-

rate shock than are value stocks. This is possibly because, as Lettau and Wachter (2007) illustrate in their

equilibrium model, growth stocks have longer durations than do value stocks. Therefore, if IPOFDR is a

proxy of conditional equity premium, its innovations should have explanatory power for the cross-section

of stock returns similar to that of HML. To address this issue, I replace HML in the Fama and French

(1996) three-factor model with IPOFDRΔ and use the new model to explain the cross-section of returns

on twenty-five Fama and French portfolios sorted by size and book-to-market equity ratio.

Table 5 reports loadings of twenty-five Fama and French portfolios on the risk factors.11 As

expected, panel A shows that value stocks have substantially higher loadings on IPOFDRΔ than do

growth stocks.12 The pattern is similar to that of loadings on HML, as reported in Table 6.

11 To address the issue of potential measurement errors in IPOFDR, I also run a 2SLS estimation using changes in

MV and IV as the instrumental variables because these two variables are closely related to IPOFDRΔ (Table 2),

and find that results are qualitatively similar to those reported in Tables 5 and 7. In particular, value stocks have

substantially higher loadings on IPOFDRΔ than do growth stocks, and IPOFDRΔ is significantly priced in the

cross-section of stock returns. For brevity, these results are not reported here but are available on request.

22

[Insert Table 5 here]

[Insert Table 6 here]

Table 7 reports the Fama and MacBeth (1973) cross-sectional regression results. For comparison,

row 1 reports the results using HML as a risk factor. Consistent with earlier studies, the risk price of HML

is positive and statistically significant at the 1% level, and the Fama and French three-factor model

accounts for about 83% of cross-sectional variation in expected stock returns. In row 2, I replace HML by

IPOFDRΔ . As expected, IPOFDRΔ is significantly priced at the 5% level, with a R2 of about 85%.

Figures 4 and 5 present the scatter plot of expected versus realized returns with IPOFDRΔ and HML as a

risk factor, respectively. They show that the two variables have similar explanatory power for the cross-

section of stock returns. To address formally this issue, I first regress HML on IPOFDRΔ and then

include the residual, HML+, in the cross-sectional regression along with IPOFDRΔ . Row 3 shows that

IPOFDRΔ remains marginally significant, while HML+ provides no incremental explanatory power.

Similarly, I also regress IPOFDRΔ on HML and then include the residual, IPOFDR+Δ , in the cross-

sectional regression along with HML. Again, row 4 shows that HML remains significant, while

IPOFDR+Δ has no incremental explanatory power. As a robustness check, I construct innovations in

IPOFDR by fitting an AR(1) model, and panel B shows that the results are essentially the same as those

12 In Table 5, I control for market returns and the size premium when estimating loadings on IPOFDRΔ . In the

univariate regression (not reported here), the relation between portfolio returns and IPOFDRΔ is always negative

because an increase in discount rates always leads to a contemporaneous capital loss. In the univariate regression,

growth stocks have a lower loading than do value stocks because the former are more sensitive to discount-rate

shocks, e.g., the capital loss is larger for growth stocks when discount rates rise. Because market returns have an

average sensitivity to discount-rate shocks, controlling for market returns allows us to demean the loadings on

IPOFDRΔ . That is, the result that value stocks have a positive loading while growth stocks have a negative loading

in Table 5 reflects the fact that growth stocks are more sensitive to discount-rate shocks than are value stocks.

23

using the first difference of IPOFDR. To summarize, IPOFDR and HML have qualitatively similar

explanatory power for the cross-section of stock returns.

[Insert Table 7 here]

[Insert Figure 4 here]

[Insert Figure 5 here]

E. IPOFDR and Expected Cash Flows

In the present-value relation, Campbell and Shiller (1988) show that the dividend yield equals

expected future dividend growth minus expected future discount rates:

(18) 1 10

[ ]1

jt t t t j t j

j

d p E d rκρ

ρ

∞

+ + + +=

⎡ ⎤⎢ ⎥− ≈− + −Δ +⎢ ⎥− ⎣ ⎦∑ .

Equation (18) indicates that the dividend yield is negatively related to future dividend growth; however,

there is rather weak empirical support for this implication. For example, row 1 of Table 8 shows that the

negative relation between the dividend yield (DP) and future dividend growth is only marginally

significant and the adjusted R2 is only 5%. One possible explanation, as suggested by Lettau and

Ludvigson (2005), is that expected dividend growth and expected discount rates are positively correlated

with each other. Consistent with the finding by Lettau and Ludvigson, row 3 shows that IPOFDR is

positively related to future dividend growth, and the relation is statistically significant at the 1% level,

with an adjusted R2 of 14%. Figure 6 also reveals a strong comovement between IPOFDR and the one-

year-ahead dividend growth.

[Insert Table 8 here]

[Insert Figure 6 here]

If there is comovement between expected returns and expected dividend growth, equation (18)

indicates that both DP and measures of ex ante equity premium should be included in the forecast of the

dividend growth if DP provides additional information. To address this issue, I include both DP and

IPOFDR as predictive variables and report the results in row 4 of Table 8. Interestingly, after controlling

24

for IPOFDR, I uncover a significantly negative relation between DP and future dividend growth, as

stipulated in equation (18). The difference between rows 1 and 4 suggests that earlier studies fail to

uncover the negative relation because of an omitted variable problem. To see this, note that DP and

IPOFDR have opposite effects on expected dividend growth, although they are positively correlated with

each other. To my best knowledge, this result is novel. As a robustness check, I also use the earning price

ratio (EP) instead of DP and find qualitatively similar results. Lastly, panel B shows that the results are

similar by using 2SLS with IV and MV as the instrumental variables for IPOFDR.

As mentioned in Section III, the results are somewhat different if I back out dividends per share

using CRSP annual total return index and annual price index. In this case, IPOFDR remains a strong

predictor of dividend growth; however, neither DP nor EP is statistically significant in the forecasting

regression. The difference reflects mainly the fact that in the construction of CRSP annual total return

index, monthly dividends are reinvested and thus compounded using market returns. As a result, the

implied annual dividend growth is closely correlated with market returns, with a correlation coefficient of

about 62% over the period 1960 to 2006, compared with only 21% if assuming that dividends are not

reinvested (Table 1). Because IPOFDR is a proxy of expected stock market returns, using non-reinvested

dividends provides a conservative estimate of the relation between expected returns and expected

dividend growth. From a theoretical point of view, i.e., equation (18), it seems to be more appropriate to

measure dividends without the reinvestment assumption than to measure dividends with the reinvestment

assumption. This difference explains why I find a significantly negative relation between DP and the

expected dividend growth using latter measure of dividends.

V. Rational versus Irrational Explanations of IPOFDR’s Information Content

I have argued that investors price IPO shares rationally and IPO underpricing moves closely with

ex ante equity premium because of partial adjustment. The view is in contrast with that by Baker and

Wurgler (2000), who suggest that investors sometimes price IPO shares irrationally and managers try to

time the market by issuing more equities when stocks are overvalued. To support this view, Baker and

25

Wurgler show that there is a significantly negative relation between the equity share of new issues and

future market returns, even after controlling for commonly used proxies of conditional equity premium,

e.g., the dividend yield and aggregate book-to-market equity ratio. Moreover, Baker and Wurgler (2006)

construct a composite investor sentiment index using six commonly used measures of investor sentiment,

including the equity share of new issues and the IPO first-day return. These authors document a strong

conditional relation between the investor sentiment index and the cross-section of stock returns. In

particular, expected returns on stocks which have highly subjective valuations and high arbitrage costs—

e.g., high volatility stocks—outperform low volatility stocks when the investor sentiment index is below

its sample average at the beginning of holding periods. High volatility stocks, however, have lower

returns when the investor sentiment index is above its sample average at the beginning of holding periods.

The evidence poses a challenge to CAPM because it requires that the market risk premium is negative in

half of the sample period. In this section, I try to reconcile the two conflicting reviews of IPOFDR’s

information content.

A. Investor Sentiment versus Omitted Risk Factors

Investor sentiment is an elusive concept. Baker and Wurgler ((2007), p. 129) define it as “a belief

about future cash flows and investment risks that is not justified by the facts at hand.” This definition is

susceptible to the classic joint hypothesis problem. The evidence that CAPM fails to explain the

predictive ability of investor sentiment for both time-series and cross-sectional stock returns implies

either (1) inefficient markets or (2) inadequacy of CAPM as an asset pricing model. That is, investor

sentiment has a pervasive effect on stock returns possibly because it is a proxy of systematic risk factors

omitted from commonly used asset pricing models.

In rational pricing models, e.g., Merton’s (1973) ICAPM, the risk premium is determined by

second moments, i.e., covariances with risk factors. By contrast, in behavioral models second moments

play no role in explaining time-series and cross-sectional stock return predictability. In the preceding

section, I use this difference to test the rational pricing interpretation against the behavioral interpretation

26

of IPOFDR’s information content in three ways. First, ceteris paribus, there is a significantly positive

relation between IPOFDR and conditional market variance. Second, the predictive power of IPOFDR for

market returns across time comes mainly from its close relation with variances of risk factors. Third, the

covariance with IPOFDR helps explain the unconditional cross-section of stock returns. These empirical

findings provide support for the rational pricing interpretation that IPOFDR is a proxy of expected

discount rates. They, however, cannot be easily reconciled with the behavioral interpretation that IPOFDR

is a measure of investor sentiment. Below, I show that other investor sentiment measures used by Baker

and Wurgler (2006) also move closely with the determinants of ex ante equity premium. I also find that

ICAPM helps explain Baker and Wurgler’s main empirical finding of a conditional relation between

investor sentiment and the cross-section of stock returns in a coherent manner.

B. Explaining Time-Series Variation in Investor Sentiment

[Insert Table 9 here]

Baker and Wurgler (2006) use six commonly used measures of investor sentiment to construct a

composite index based on the first principal component. Table 9 investigates whether these measures are

correlated with the determinants of equity premium—i.e., MV and IV.13 CEFD is the close-end fund

discount; TURN is the NYSE share turnover; NIPO is the number of IPOs; IPOFDR is the IPO first-day

return; S is the equity share in new issues; PDND is dividend premium—the log difference of the average

market-to-book equity ratio between dividend payers and nonpayers; and SENT is the composite investor

sentiment index. Baker and Wurgler also construct a second index—SENT⊥ —by removing cyclical

variation from each of the six investor sentiment measures prior to the principal components analysis.

Because the cyclical component may be related to discount rates, Baker and Wurgler argue that SENT⊥

is a cleaner measure of investor sentiment. Because NIPO takes only integral values, its distribution is

likely to be very different from that of a normal distribution in small sample. To address this issue, I also

13 I thank Jeffrey Wurgler for providing investor sentiment data over the 1962 to 2005 period.

27

use a log transformation, LNIPO, in the empirical analysis. Note that TURN, NIPO, and S are positively

correlated with SENT, while the relation is negative for CEFD, IPOFDR, and PDND. Below I test the

conjecture of a negative relation between investor sentiment and ex ante equity premium.

As hypothesized, Table 9 shows that there is a strong relation between SENT and the

determinants of equity premium. In particular, SENT is positively correlated with IV and is negatively

correlated with MV, with an adjusted R2 of about 20%. Thus investor sentiment tends to be high when

expected equity premium is low. This result confirms that standard measures of investment sentiment do

have close correlation with conditional equity premium; however, it casts doubt on the interpretation that

SENT measures “belief about future cash flows and investment risks that is not justified by the facts at

hand.” Interestingly, the results are essentially the same for SENT⊥ , even though cyclical variation has

been explicitly purged out from the variable. Table 9 also shows that most of individual measures of

investor sentiment are strongly correlated with IV and MV with expected signs. Note that IPOFDR has

the largest adjusted R2 among all measures of investor sentiment, including the composite indices. This

result suggests that IPOFDR has the closest relation with ex ante equity premium possibly because it is a

theoretically motivated variable, as explained in Section II. Consistent with this conjecture, I show next

that IPOFDR also has the strongest predictive power for stock market returns among all measures of

investor sentiment considered in Baker and Wurgler (2006).

C. Investor Sentiment and Future Market Returns

[Insert Table 10 here]

This subsection investigates the information content of investor sentiment for future excess stock

market returns. Panel A of Table 10 compares the predictive power of SENT, SENT⊥ , and S with that of

IPOFDR. Row 1 replicates Baker and Wurgler’s (2000) main finding of a negative relation between S and

one-year-ahead excess market returns. As expected, SENT and SENT⊥ correlate negatively with future

market returns, although the relations are statistically insignificant (rows 2 and 3). The weak relation may

28

reflect the fact that the investor sentiment indexes are noisy measures of ex ante equity premium. To

address this issue, I use 2SLS with lagged IV and MV as the instrumental variables and find that the

negative relation become statistically significant at the 1% level for both SENT and SENT⊥ . For brevity,

this result is not reported here but is available on request.

Table 10 shows that both one-period and two-period lagged IPOFDRs forecast market returns

(rows 4 and 5). The Wald test indicates that they jointly have significant predictive power at the 1% level

(row 6). Interestingly, after controlling for two lags of IPOFDR, the predictive power of S becomes

statistically insignificant at the 10% level (row 7). Because IPOFDR is arguably a proxy of ex ante equity

premium, this result casts doubt on Baker and Wurgler’s (2000) interpretation that managers issue more

new equities when stocks are overvalued. By contrast, the result is consistent with the theoretical models

by Pastor and Veronesi (2005) and Zhang (2005), who argue for a close relation between IPO waves and

discount rates. Similarly, after controlling for IPOFDR, the relation between SENT and future market

returns becomes positive albeit statistically insignificant. I find similar results using 2SLS with lagged IV

and MV as the instrumental variables (not reported). Thus, the negative relation between SENT and

future market returns comes mainly from the strong comovement between SENT and ex ante equity

premium. Again, row 9 shows that the result is qualitatively similar for SENT⊥ .

Panel B of Table 10 shows that individually none of other investor sentiment measures has

statistically significant predictive power for market returns. PDND becomes significantly negative when

combined with two lags of IPOFDR; however, the negative effect is at odds with the interpretation that

PDND comoves negatively with investor sentiment.

To summarize, among all measures of investment sentiment considered by Baker and Wurgler

(2006), IPOFDR has the strongest predictive power for market returns.

29

D. Conditional Relation between Investor Sentiment and Cross-Section of Stock Returns

Baker and Wurgler (2006) find that when the beginning-of-period investor sentiment index is

above its sample average, subsequent returns are lower on “risky” (e.g., small, young, high volatility,

unprofitable, non-dividend-paying, extreme-growth, and distressed) stocks than on “safe” (e.g., large, old,

and low volatility) stocks. The patterns, however, largely reverse when investor sentiment is below the

sample average. One possible explanation, as advanced by Baker and Wurgler, is that because risky

stocks tend to have highly subjective valuations and high arbitrage costs, they are more susceptible to

swings in investor sentiment than are safe stocks. In particular, these authors suggest that unsophisticated

investors prefer risky stocks when investor sentiment is high but demand safe stocks when investor

sentiment is low. Therefore, when investor sentiment is above the sample average, risky stocks tend to

have lower returns than do safe stocks in the following period because the relative demand for risky

stocks decreases as investor sentiment falls eventually.14 Conversely, when investor sentiment is below

the sample average, returns on risky stocks are likely to be higher than are returns on safe stocks in the

following period because the relative demand for risky stocks increases as investor sentiment rises

eventually.

In subsections V.B and V.C, I document a close (negative) relation between investor sentiment

and conditional equity premium. Using this relation, I argue that Baker and Wurgler’s (2006) findings

indicate that risky stocks are more sensitive to discount-rate shocks than are safe stocks because the

former tend to have longer durations (e.g., Cornell (1999) and Dechow, Sloan, and Soliman (2004)). The 14 When investor sentiment is above the sample average, it is more likely to fall than to rise in the following period

for two reasons. First, investor sentiment is stationary and follows a mean-reverting process. Second, Baker and

Wurgler (2006) sort investor sentiment using the full sample; therefore, by construction, investor sentiment is more

likely to decrease than to increase in the following period when it is currently above the sample average. For

example, when investor sentiment has the highest value of the whole sample, the probability that it will decrease in

the following period equals one. Similarly, when investor sentiment is low, by construction, it is more likely to

increase than to decrease in the following period.

30

main idea is as follows. When investor sentiment is high or discount rates are low, discount rates are more

likely to increase than to decrease subsequently. Thus stocks are likely to have a below average return in

the following period as discount rates rise; and the negative effect is more pronounced for risky stocks

than for safe stocks because, as hypothesized, the former are more sensitive to discount-rate shocks.

Conversely, when investor sentiment is low or discount rates are high, discount rates are more likely to

fall than to rise subsequently. Thus stocks are likely to have an above average return in the following

period as discount rates fall; the positive effect is again more pronounced for risky stocks than for safe

stocks because the former are more sensitive to discount-rate shocks.15

I test this alternative hypothesis in three ways using equal-weighted returns on quintile portfolios

sorted by idiosyncratic stock volatility. First, I regress the portfolio return on IPOFDRΔ , and the

estimated coefficient on IPOFDRΔ is a measure of sensitivity to discount-rate shocks. The coefficient is

negative for all portfolios because an increase in discount rates leads to a contemporaneous capital loss.

More importantly, it decreases monotonically from the quintile of stocks with the lowest volatility (–0.22)

to the quintile of stocks with the highest volatility (–1.52), indicating that, as hypothesized, high volatility

stocks are more sensitive to discount-rate shocks than are low volatility stocks. As a robustness check, I

also use the fitted value from the regression of excess market returns on lagged IV and MV as a measure

of conditional equity premium, and find qualitatively similar results. Second, consistent with Baker and

Wurgler (2006), the annual return difference between the quintiles of highest and lowest volatility stocks

is –10.1% when investor sentiment is above the sample average and is 14.5% when investor sentiment is 15 Figure 2 in Baker and Wurgler (2006) shows that for most portfolios, returns are higher when the beginning-of-

period investor sentiment is below the sample average than when the beginning-of-period investor sentiment is

above the sample average. While this finding is a direct implication of the conjecture that investor sentiment is

negatively correlated with discount rates, it appears to be inconsistent with Baker and Wurgler’s conjecture that

unsophisticated investors’ relative demand for safe stocks increases (decreases) when investor sentiment falls (rises).

In particular, according to Baker and Wurgler’s conjecture, safe stocks should have above instead of below average

returns when investor sentiment is high at the beginning of holding periods.

31

below the sample average. I find a similar result using IPOFDR or the estimated conditional equity

premium based on IV and MV as the conditioning variable. For example, the return difference is –9.1%

when the estimated conditional equity premium is below the sample average and is 13.8% when the

estimated conditional equity premium is above the sample average. Lastly, I regress investor sentiment on

IPOFDR, IV, MV, and NIPO, and find that the residual from the regression has negligible explanatory

power for the cross-section of portfolio returns.16 The result indicates that investor sentiment explains the

cross-section of stock returns mainly because of its negative correlation with conditional equity premium.

Baker and Wurgler (2006) also provide formal statistical evidence that investor sentiment

forecasts returns on a hedge portfolio that is long in high volatility stocks and short in low volatility

stocks. I confirm their finding by documenting a significantly negative relation between the two variables.

Interestingly, IPOFDR correlates positively and significantly with future portfolio returns as well.

Moreover, after I control for IPOFDR, the predictive power of investor sentiment becomes statistically

insignificant. Lastly, MV and IV jointly have significant forecasting power for the portfolio return, with a

positive relation for MV and a negative relation for IV.

In Merton’s (1973) ICAPM, the conditional excess portfolio return depends on its conditional

covariance with excess market returns if changes in the set of investment opportunities have a negligible

effect on expected stock returns

(19) 2, 1 , 1 , 1 , , ,( ) cov( , )t i t i t M t i M t M tE r r rγ γβ σ+ + += = ,

where γ is a measure of relative risk aversion and 2,M tσ is conditional market variance. As pointed out by

Baker and Wurgler (2006), their results suggest that either (1) , ,i M tβ moves closely with investor

sentiment or (2) the conditional market risk premium, 2,M tγσ , is negative in half of the sample period.

Because Baker and Wurgler find little empirical support for time-varying , ,i M tβ , they conclude that

16 Pastor and Veronesi (2005), Zhang (2005), and Carson, Fisher, and Giammarino (2006) argue that time-varying

discount rates are a main driver of IPO volumes.

32

CAPM cannot explain their main findings because 2,M tγσ should be always positive. However, their

results are potentially consistent with ICAPM

(20) 2 2, 1 , , , , , ,( )t i t i M t M t i H t H tE r γβ σ λβ σ+ = + ,

where λ is the price of risk for the hedging risk factor, , ,i H tβ is the loading on the hedging risk factor, and

2,H tσ is the conditional variance of the hedging risk factor. Guo and Savickas (2008) argue that MV and

IV jointly forecast market returns because they are proxies of 2,M tσ and 2

,H tσ , respectively. Therefore, I

can write an empirical specification of conditional equity premium as

(21) , 1 , ,IV( ) MV IV MV ( )

MVt

t M t t M H t t M Ht

E r γ λβ γ λβ+ = + = + .

For simplicity, in equation (21), I assume that loadings of market returns on the hedge factor are constant.

Consistent with ICAPM, Guo and Savickas (2008) find that MV is positively correlated with future

market returns. The relation, however, is negative for IV, indicating that the market serves as a hedge for

changes in the set of investment opportunities. Equation (21) shows that conditional equity premium is

high (low) when MV is high (low) relative to IV. Similarly, the conditional return difference between

high and low volatility stocks can be written as

(22) 5, 1 1, 1 5, 1, 5, 1,

5, 1, 5, 1,

( ) ( ) MV ( ) IVIVMV [( ) ( ) ]

MV

t t t M M t H H t

tt M M H H

t

E r r β β γ β β λ

β β γ β β λ

+ +− = − + −

= − + −,

where 5,Mβ ( 5,Hβ ) and 1,Mβ ( 1,Hβ ) are loadings on market (hedge) risk for the high and low volatility

stocks, respectively. As mentioned above, the return difference between high and low volatility stocks is

positively correlated with MV and is negatively correlated with IV in data. That is, 5, 1,( )M Mβ β γ− is

positive and 5, 1,( )H Hβ β λ− is negative. Therefore, when conditional equity premium is high or when MV

is high relative to IV, high volatility stocks are likely to have higher expected returns than are low

volatility stocks. Conversely, when conditional equity premium is low or when MV is low relatively to

IV, high volatility stocks are likely to have lower expected returns than are low volatility stocks.

33

Therefore, by contrast with CAPM, to explain Baker and Wurgler’s findings, ICAPM does not require

either (1) that 2,M tγσ is negative for half of the sample period or (2) that factor loadings change with

investor sentiment across time. To illustrate formally the point, I use the fitted value from the regression

of portfolio returns on lagged IV and MV as a measure of conditional portfolio returns. The average of

estimated conditional equity premium is 8.5% when investor sentiment is below the sample average,

compared with 2.7% when investor sentiment is above the sample average. Moreover, the average of

estimated conditional returns on the portfolio that is short in low volatility stocks and long in high

volatility stocks is 5.4% when investor sentiment is below the sample average, compared with –1.3%

when investor sentiment is above the sample average.

[Insert Table 11 here]

Baker and Wurgler (2006) use equal-weighted portfolio returns in their empirical analysis. As a

robustness check, I show in Table 11 that results are qualitatively similar using value-weighted portfolio

returns. I first replicate Baker and Wurgler’s main finding that SENT forecasts IVF—the return difference

between stocks with high and low volatility (row 1).17 In particular, the relation is negative, indicating that

stocks with high volatility tend to have relatively low returns when investor sentiment is high at the

beginning of holding periods. Row 2 shows that IPOFDR—a measure of ex ante equity premium—has

significant explanatory power for IVF as well. Similarly, IV and MV jointly forecast IVF; in particular,

while IV is negatively related to one-year-ahead IVF, the relation is positive for MV (row 3). These

results confirm that high volatility stocks have relatively low returns when discount rates are low at the

beginning of holding periods.

Pastor and Veronesi (2003) show that stocks with high volatility tend to be small young growth

stocks. These stocks are likely to be more sensitive to changes in discount rates than are stocks with low

volatility because the former tend to have longer durations. Therefore, if IPOFDRΔ is a measure of

17 I find qualitatively similar results for portfolios sorted by dividends and earnings. For brevity, these results are not

reported here but are available on request.

34

discount rate shocks, it should be negatively correlated with IVF. I confirm this conjecture in row 4 of

Table 11. In rows 5 to 7, I investigate whether predictors of market returns forecast residuals from the

regression in row 4. In particular, Baker and Wurgler (2006) suggest that SENT should forecast the

residual that are uncorrected with systematic risk. After controlling for IVF’s comovement with

IPOFDRΔ as well as other risk factors, the predictive power of SENT for one-year-ahead IVF becomes

statistically insignificant at the 5% level (row 5), and the adjusted R2 decreases sharply to less than 4%

from 23% in row 1. The results are qualitatively similar for IPOFDR (row 6) and IV and MV (row 7).

Therefore, by contrast with Baker and Wurgler’s conjecture, the predictive power of investor sentiment

reflects mainly systematic risk.

Lastly, Baker and Wurgler (2006) find that the return difference between high and low investor

sentiment states is a U-shaped function of B/M. These authors argue that stocks with extreme values of

B/M are more susceptible to swings in investor sentiment than are stocks with median B/M. Alternatively,

the finding may suggest that stocks with extreme values of B/M are more sensitive to discount-rate

shocks than are stocks with median B/M. Again, I test this alternative hypothesis using equal-weighted

returns on quintile portfolios sorted by B/M. First, I regress the portfolio returns on IPOFDRΔ and find

that the coefficient is negative for all portfolios. Interestingly, the coefficient is also a U-shaped function

of B/M: It equals –1.03 for extreme growth stocks, –0.55 for stocks with median B/M, and –0.64 for

stressed stocks.18 Second, using either IPOFDR or the estimated conditional equity premium based on IV

and MV as the conditioning variable, I find that the return difference between high and low conditional 18 The pattern is somewhat different from that reported in Table 5, which shows that loadings on IPOFDRΔ tend to

increase monotonically with B/M within each size quintile. There are three explanations for the difference. First, in

Table 5, the portfolios are constructed using two independent sorts—by size and by B/M. Second, in Table 5, I use

value-weighted portfolio returns instead of equal-weighted portfolio returns. Third, in Table 5, I control for market

risk and the size premium when estimating loadings on IPOFDRΔ . Nevertheless, for equal-weighted quintile

portfolios sorted by B/M, loadings of extreme growth stocks on discount-rate shocks are substantially smaller than

are those of stressed stocks, and the difference is statistically significant at the 10% level.

35

equity premium states is a U-shaped function of B/M as well. Third, if I regress investor sentiment on

IPOFDR, IV, MV, and NIPO, the residual has negligible explanatory power for the cross-section of stock

returns. Lastly, I replicate Baker and Wurgler’s findings that investor sentiment is negatively correlated

with future return difference between extreme growth stocks (or distressed stocks) and stocks with

median B/M; its predictive power, however, becomes negligible after controlling for IPOFDR in the

forecasting regression. Therefore, both extreme growth and distressed firms’ stock returns are high

relative to their unconditional average when sentiment is low because these stocks are more sensitive to

discount-rate shocks than are stocks with median B/M.

To summarize, because of the close relation between investor sentiment and conditional equity

premium, ICAPM explains Baker and Wurgler’s (2006) main findings of a conditional relation between

investor sentiment and the cross-section of stock returns in a coherent manner.

VI. Conclusion

In this paper, I propose a new forecasting variable of stock market returns, IPOFDR, which is

constructed using the average IPO first-day return. Unlike other predictive variables considered in the

existing literature, I argue that IPOFDR is a direct measure of ex ante equity premium. Consistent with

this conjecture, IPOFDR is closely correlated with measures of stock market risk; has significant

predictive ability for stock market returns in sample and out of sample; and helps explain the cross-

section of stock returns. These results suggest that conditional equity premium does change across time

and the hedging demand for time-varying equity premium has significant effects on stock prices.

The empirical findings in this paper shed light on two important questions about efficient markets

hypothesis. The first question is whether stock market returns are predictable across time. Financial

economists have long believed that expected market returns are constant. In the past two decades, inspired

by seminar works of Campbell and Shiller (1988) and Fama and French (1989), researchers have found

that many variables appear to have significant predictive ability for market returns. However, Goyal and

36

Welch (2008) comprehensively reexamine the existing empirical studies and find no reliable evidence of

stock return predictability, especially in the out-of-sample context. Cochrane (2008), Campbell (2008),

and Pastor and Stambaugh (2009) argue that stock returns are predictable by using more powerful tests. In

this paper, I propose a theoretically motivated variable and show that it forecasts stock market returns in

and out of sample. The result confirms that stock market returns are predictable.

The second question is whether stock return predictability poses a challenge to efficient markets

hypothesis. Fama and French (1989) and many other argue that conditional equity premium moves

countercyclically across business cycles. Moreover, Campbell and Cochrane (1999) and Bansal and

Yaron (2004), among others, develop equilibrium models to explain the countercyclical variation in

conditional equity premium. Some other authors, however, argue that stock return predictability mainly

reflects mispricing or investor sentiment. For example, Baker and Wurgler (2000) argue that the equity

share of new issues forecasts market returns because managers try to time the market by issuing more

new equities when stocks are overvalued. I cast doubt on this interpretation by showing that the equity

share of new issues forecasts stock returns mainly because of its close correlation with IPOFDR—a proxy

of ex ante equity premium. Moreover, I find that commonly used measures of investor sentiment move

closely with the determinants of conditional equity premium. These results suggest that mispricing is

unlikely to be an important driver of stock return predictability.

37

References

Andersen, T.; T. Bollerslev; F. Diebold; and P. Labys. “Modeling and Forecasting Realized Volatility.”

Econometrica, 71 (2003), 579-625.

Baker, M., and J. Wurgler. “The Equity Share in New Issues and Aggregate Stock Returns.” Journal of

Finance, 55 (2000), 2219-2257.

Baker, M., and J. Wurgler. “Investor Sentiment and the Cross-Section of Stock Returns.” Journal of

Finance, 61 (2006), 1645-1680.

Baker, M., and J. Wurgler. “Investor Sentiment in the Stock Market.” Journal of Economic Perspectives,

21 (2007), 129-151.

Bansal, R., and A. Yaron. “Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles.”

Journal of Finance, 59 (2004), 1481-1509.

Benveniste, L., and P. Spindt. “How Investment Bankers Determine the Offer Price and Allocation of

New Issues.” Journal of Financial Economics, 24 (1989), 343-361.

Bradley, D., and B. Jordan. “Partial Adjustment to Public Information and IPO Underpricing.” Journal of

Financial and Quantitative Analysis, 37 (2002), 595-616.

Carlson, M.; A. Fisher; and R. Giammarino. “Corporate Investment and Asset Price Dynamics:

Implications for SEO Event Studies and Long-Run Performance.” Journal of Finance, 61 (2006),

1009–1034.

Campbell, J. “Stock Returns and the Term Structure.” Journal of Financial Economics, 18 (1987), 373-

399.

Campbell, J. “Intertemporal Asset Pricing without Consumption Data.” American Economic Review, 83

(1993), 487-512.

Campbell, J. “Estimating the Equity Premium.” Canadian Journal of Economics, 41 (2008),1-21.

Campbell, J., and J. Cochrane. “By Force of Habit: A Consumption-Based Explanation of Aggregate

Stock Market Behavior.” Journal of Political Economy, 107 (1999), 205-251.

38

Campbell, J., and R. Shiller. “The Dividend-Price Ratio and Expectations of Future Dividends and

Discount Factors.” Review of Financial Studies, 1 (1988), 195-228.

Campbell, J., and T. Vuolteenaho. “Bad Beta, Good Beta.” American Economic Review, 94 (2004), 1249-

1275.

Cao, C.; T. Simin; and J. Zhao. “Can Growth Options Explain the Trend in Idiosyncratic Risk?” Review

of Financial Studies, 21 (2008), 2599-2633.

Clark, T., and M. McCracken. “Tests of Equal Forecast Accuracy and Encompassing for Nested Models.”

Journal of Econometrics, 105 (2001), 85-110.

Cochrane, J. “The Dog That Did Not Bark: A Defense of Return Predictability.” Review of Financial

Studies, 21 (2008), 1533-1575.

Cornell, B. “Risk, Duration, and Capital Budgeting: New Evidence on Some Old Questions.” Journal of

Business, 72 (1999), 183-200.

Dechow, P.; R. Sloan; and M. Soliman. “Implied Equity Duration: A New Measure of Equity Risk.”

Review of Accounting Studies, 9 (2004), 197–228.

Edelen, R., and G. Kadlec. “Issuer Surplus and the Partial Adjustment of IPO Prices to Public

Information.” Journal of Financial Economics, 77 (2004), 347-373.

Fama, E., and K. French. “Dividend Yields and Expected Stock Returns.” Journal of Financial

Economics, 22 (1988), 3-25.

Fama, E., and K. French. “Business Conditions and Expected Returns on Stocks and Bonds.” Journal of

Financial Economics, 25 (1989), 23-49.

Fama, E., and K. French. “Multifactor Explanations of Asset Pricing Anomalies.” Journal of Finance, 51

(1996), 55-84.

Fama E., and J. MacBeth. “Risk, Return, and Equilibrium: Empirical Tests.” Journal of Political

Economy, 81 (1973), 607-636.

French, K.; W. Schwert; and R. Stambaugh. “Expected Stock Returns and Volatility.” Journal of

Financial Economics, 19 (1987), 3-30.

39

Glosten, L.; R. Jagannathan; and D. Runkle. “On the Relation between the Expected Value and the

Volatility of the Nominal Excess Return on Stocks.” Journal of Finance, 48 (1993), 1779-1801.

Goyal, A., and I. Welch. “A Comprehensive Look at the Empirical Performance of Equity Premium

Prediction.” Review of Financial Studies, 21 (2008), 1455-1508.

Guo, H., and R. Savickas. “Average Idiosyncratic Variance in G7 Countries.” Review of Financial

Studies, 21 (2008), 1259-1296.

Guo, H., and R. Whitelaw. “Uncovering the Risk-Return Relation in the Stock Market.” Journal of

Finance, 61 (2006), 1433-1463.

Hahn, J., and H. Lee. “Yield Spreads as Alternative Risk Factors for Size and Book-to-Market.” Journal

of Financial and Quantitative Analysis, 41 (2006), 245-269.

Hanley, K. “The Underpricing of Initial Public Offerings and the Partial Adjustment Phenomenon.”

Journal of Financial Economics, 34 (1993), 231-250.

Ibbotson, R. “Price Performance of Common Stock New Issues.” Journal of Financial Economics, 2

(1975), 235-272.

Lettau, M., and S. Ludvigson. “Consumption, Aggregate Wealth, and Expected Stock Returns.” Journal

of Finance, 56 (2001), 815-849.

Lettau, M., and S. Ludvigson. “Expected Returns and Expected Dividend Growth.” Journal of Financial

Economics, 76 (2005), 583-626.

Lettau, M., and J. Wachter. “Why Is Long-Horizon Equity Less Risky? A Duration-Based Explanation of

the Value Premium.” Journal of Finance, 62 (2007), 55-92.

Ljungqvist, A. “IPO Underpricing.” Working Paper, New York University (2004).

Ljungqvist, A.; V. Nanda; and R. Singh. “Hot Markets, Investor Sentiment, and IPO Pricing.” Journal of

Business, 79 (2006), 1667-1702.

Logue, D. “Premia on Unseasoned Equity Issues, 1965-69.” Journal of Economics and Business, 25

(1973), 133-141.

40

Loughran, T., and J. Ritter. “Why Don’t Issuers Get Upset About Leaving Money on the Table in IPOs?”

Review of Financial Studies, 15 (2002), 413-443.

Lowry, M. “Why Does IPO Volume Fluctuate So Much?” Journal of Financial Economics, 67 (2003), 3-

40.

Lowry, M., and G. Schwert. “Is the IPO Pricing Process Efficient?” Journal of Financial Economics, 71

(2004), 3-26.

Lowry, M., and S. Shu. “Litigation Risk and IPO Underpricing.” Journal of Financial Economics, 65

(2002), 309-335.

Lyandres, E.; L. Sun; and L. Zhang. “The New Issues Puzzle: Testing the Investment-Based

Explanation.” Review of Financial Studies, 21 (2008), 2825-2855.

McCracken, M. “Asymptotics for Out-of-Sample Tests of Granger Causality.” Working Paper, Louisiana

State University (1999).

Merton, R. “An Intertemporal Capital Asset Pricing Model.” Econometrica, 41 (1973), 867-887.

Merton, R. “On Estimating the Expected Return on the Market: An Exploratory Investigation.” Journal of

Financial Economics, 8 (1980), 323-361.

Miller, E. “Risk, Uncertainty, and Divergence of Opinion.” Journal of Finance, 32 (1977), 1151-1168.

Pastor, L., and P. Veronesi. “Stock Valuation and Learning about Profitability.” Journal of Finance, 58

(2003), 1749-1790.

Pastor, L., and P. Veronesi. “Rational IPO waves.” Journal of Finance, 60 (2005), 1713-1757.

Pastor, L. and R. Stambaugh. “Predictive Systems: Living with Imperfect Predictors.” Journal of

Finance, 64 (2009), 1583-1628.

Pastor, L.; M. Sinha; and B. Swaminathan. “Estimating the Intertemporal Risk-Return Tradeoff Using the

Implied Cost of Capital.” Journal of Finance, 63 (2008), 2859-2897.

Petkova, R. “Do the Fama-French Factors Proxy for Innovations in Predictive Variables?” Journal of

Finance, 61 (2006), 581-612.

41

Ritter, J. “The Long-Run Performance of Initial Public Offerings.” Journal of Finance, 46 (1991), 3-

27.

Ritter, J. “Investment Banking and Securities Issuance.” in Handbook of the Economics of Finance, G.M.

Constantinides, M. Harris, and R. Stulz, eds. North-Holland (2003).

Ritter, J., and I. Welch. “A Review of IPO Activity, Pricing, and Allocations.” Journal of Finance, 57

(2002), 1795-1828.

Rock, K. “Why New Issues Are Underpriced.” Journal of Financial Economics, 15 (1986), 187-212.

Tinic, S. “Anatomy of Initial Public Offerings of Common Stock.” Journal of Finance, 43 (1988), 789–

822.

Scruggs, J. “Resolving the Puzzling Intertemporal Relation between the Market Risk Premium and

Conditional Market Variance: A Two Factor Approach.” Journal of Finance, 53 (1998), 575-603.

Scruggs, J., and P. Glabadanidis. “Risk Premia and the Dynamic Covariance between Stock and Bond

Returns.” Journal of Financial and Quantitative Analysis, 38 (2003), 295-316.

Shleifer, A., and R. Vishny. “The Limits of Arbitrage.” Journal of Finance, 52 (1997), 35–55.

Welch, I. “Sequential sales, Learning, and Cascades.” Journal of Finance, 47 (1992), 695–732.

Whitelaw, R. “Time Variations and Covariations in the Expectation and Volatility of Stock Market

Returns.” Journal of Finance, 49 (1994), 515-541.

Zhang, L. “Anomalies.” Working Paper 11322, National Bureau of Economic Research (2005).

42

Figure 1

Standardized IPOFDR (Solid Line) and Number of IPOs

Figure 2

Realized Market Variance (Solid Line) and Average Idiosyncratic Variance

0

200

400

600

800

1000

-6

-4

-2

0

2

4

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

0

0.02

0.04

0.06

0.08

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

43

Figure 3

Standardized IPOFDR (Solid Line) and Standardized One-Year-Ahead Excess Market Returns

Figure 4

Expected (Vertical Axis) versus Realized (Horizontal Axis) Returns with IPOFDR as a Risk Factor

-4

-2

0

2

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

0

0.06

0.12

0.18

0 0.06 0.12 0.18

44

Figure 5

Expected (Vertical Axis) versus Realized (Horizontal Axis) Returns with HML as a Risk Factor

Figure 6

Standardized IPOFDR (Solid Line) and Standardized One-Year-Ahead Dividend Growth

0

0.06

0.12

0.18

0 0.06 0.12 0.18

-4

-2

0

2

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

45

Table 1

Summary Statistics

IPOFDR ERET DIVΔ HML IPOFDRΔ Panel A Univariate Statistics

Mean -0.170 0.059 0.014 0.066 0.002 Standard Deviation

0.151 0.165 0.044 0.138 0.160

Autocorrelation 0.442 -0.041 0.658 -0.089 -0.076

Panel B Cross Correlation

IPOFDR 1.000 ERET -0.156 1.000

DIVΔ 0.209 0.209 1.000 HML 0.316 -0.294 -0.016 1.000

IPOFDRΔ 0.531 -0.484 -0.178 0.490 1.000 Note: The table provides summary statistics of some selected variables used in this paper. IPOFDR is minus average

IPO first-day return; ERET is excess stock market returns; DIVΔ is the growth rate of dividends per share; HML is

the high-minus-low factor in the Fama and French (1996) three-factor model; and IPOFDRΔ is the first difference

of IPOFDR. The annual data span the 1960 to 2006 period.

46

Table 2

Explaining Time-Series Variation in IPOFDR

IV MV Wald Test (p-value)

2R

Panel A 1 1 1IPOFDR MVt t tθ γ η+ + += + +

1960-2005 2.349 (2.338)

-0.016

1960-1982 2.094 (3.486)

-0.045

1983-2005 2.543 (2.883)

-0.036

1960-1995 1.156 (1.991)

-0.028

Panel B 1 1 1IPOFDR MVt t tθ γ η+ + +Δ = + Δ +

1960-2005 0.258 (2.506)

-0.023

1960-1982 2.207 (3.599)

-0.044

1983-2005 -0.730 (3.207)

-0.046

1960-1995 0.859 (1.481)

-0.028

Panel C 1 1 1 1IPOFDR MV IVt t t tθ γ δ η+ + + += + + +

1960-2005 -10.083** (2.441)

13.508** (3.913)

17.084 (0.000)

0.330

1960-1982 -24.730* (11.213)

25.925* (10.216)

6.621 (0.037)

0.176

1983-2005 -10.887** (2.943)

14.783** (5.168)

30.414 (0.000)

0.615

1960-1995 -13.519* (6.856)

15.677* (6.438)

6.310 (0.043)

0.091

Panel D 1 1 1 1IPOFDR MV IVt t t tθ γ δ η+ + + +Δ = + Δ + Δ +

1960-2005 -9.396* (4.528)

11.296* (4.738)

5.689 (0.058)

0.149

1960-1982 -24.280** (8.936)

19.108** (7.136)

7.923 (0.019)

0.097

1983-2005 -8.658 (4.990)

11.609* (5.820)

4.010 (0.135)

0.236

1960-1995 -13.739* (5.447)

13.701* (5.756)

6.362 (0.042)

0.074

47

Note: The table reports the OLS estimation results of regressing IPOFDR on stock market variance (MV) and

average idiosyncratic variance (IV). Panels A and C use levels and Panels B and D use the first difference. IPOFDR

is minus average IPO first-day returns. White-corrected standard errors are reported in parentheses. Asterisks * or **

indicate significance at the 5% and 1% levels, respectively.

48

Table 3

Forecasting One-Year-Ahead Excess Stock Market Returns: OLS Regressions

IPOFDR IPOFDR*DUM +γ δ 2RPanel A 1 1ERET IPOFDRt t tθ γ η+ += + +

1961-2006 0.392** (0.119)

0.108

1961-1982 0.317 (0.201)

0.038

1983-2006 0.501** (0.087)

0.187

1961-1995 0.355 (0.194)

0.051

Panel B 1 1ERET IPOFDR IPOFDR *DUMt t t t tθ γ δ η+ += + + +

1961-2006 0.407** (0.114)

-0.177 (0.182)

0.230 (0.211)

0.096

1961-1982 0.412* (0.171)

-0.403* (0.182)

0.009 (0.247)

0.053

1983-2006 0.524** (0.092)

0.327 (0.743)

0.850 (0.779)

0.160

1961-1995 0.442* (0.177)

-0.347* (0.171)

0.095 (0.209)

0.061

Note: The table reports the OLS estimation results of forecasting one-year ahead excess market returns (ERET).

IPOFDR is minus average IPO first-day returns and DUM is a dummy variable, which equals one for the years

during which the number of IPOs is less than 200 and equals zero otherwise. White-corrected standard errors are

reported in parentheses. Asterisks * or ** indicate significance at the 5% and 1% levels, respectively.

49

Table 4

Tests of Out-of-Sample Forecast Performance

ENC-NEW MSE-F Models AMSE / BMSE Statistic BS.

CV

Statistic BS. CV

1 C+IPOFDR vs. C 0.852 4.220 2.503 5.197 1.625 2 C+IPOFDR+IPOFDR*DUM vs. C 0.862 5.132 3.551 4.876 1.622

Note: Expected excess stock market returns are constant in the benchmark model. I augment the benchmark model

with IPOFDR in row 1 and with IPOFDR and IPOFDR*DUM in row 2. IPOFDR is minus average IPO first-day

returns and DUM is a dummy variable, which equals one for the years during which the number of IPOs is less than

200 and equals zero otherwise. I report three out-of-sample forecast tests: (1) the mean-squared forecasting error

(MSE) ratio of the augmented model to the benchmark model, AMSE / BMSE , (2) the encompassing test ENC-

NEW developed by Clark and McCracken (2001); and (3) the equal forecast accuracy test MSE-F developed by

McCracken (1999). I use observations over the period 1961 to 1977 for the initial in-sample estimation and then

generate forecasts recursively for stock returns over the period 1978 to 2006. The BS. CV column reports the

empirical 95 percent critical values obtained from the bootstrapping, as in Lettau and Ludvigson (2001). In

particular, I first estimate a VAR (1) process of excess stock market returns and its forecasting variables with the

restrictions under the null hypothesis. I then feed the saved residuals with replacements to the estimated VAR

system, of which I set the initial values to their unconditional means. The ENC-NEW and MSE-F statistics are

calculated using the simulated data and the whole process is repeated 10,000 times.

50

Table 5

Loadings of Portfolios Sorted on Size and Book-to-Market on Changes in IPOFDR

1 (low B/M)

2 3 4 5 (high B/M)

5-1

Panel A Loadings on IPOFDRΔ

1 (small cap) -0.340 0.012 0.138 0.296 0.278 0.618 2 -0.159 0.080 0.193 0.353 0.401 0.559 3 -0.197 0.108 0.236 0.356 0.352 0.548 4 -0.262 0.135 0.317 0.286 0.253 0.515

5 (large cap) -0.064 0.097 0.009 0.265 0.292 0.355 5-1 0.276 0.085 -0.130 -0.031 0.014

Panel B Loadings on ERET

1 (small cap) 1.092 1.064 0.898 0.906 0.992 -0.099 2 1.078 0.924 0.941 0.970 1.003 -0.075 3 1.009 0.920 0.856 0.982 0.865 -0.144 4 0.928 0.907 0.963 0.966 0.994 0.066

5 (large cap) 1.064 0.995 0.833 0.954 1.017 -0.047 5-1 -0.028 -0.069 -0.065 0.048 0.025

Panel C Loadings on SMB

1 (small cap) 1.607 1.585 1.385 1.381 1.470 -0.137 2 1.110 0.985 1.100 0.994 1.034 -0.076 3 0.728 0.821 0.731 0.845 0.955 0.227 4 0.406 0.447 0.540 0.549 0.573 0.167

5 (large cap) -0.138 0.030 0.011 0.116 0.118 0.256 5-1 -1.745 -1.555 -1.374 -1.264 -1.352

Note: The table reports loadings of twenty-five Fama and French (1996) portfolios on risk factors:

, 1 1 1 2 1 3 1 1IPOFDR MKT SMBpi t t t t tR α β β β η+ + + + += + Δ + + + ,

where IPOFDRΔ is the first difference of IPOFDR; ERET is the excess stock market return; and SMB is the small-

minus-big factor. The annual data span the period 1960 to 2006.

51

Table 6

Loadings of Portfolios Sorted on Size and Book-to-Market on HML

1 (low B/M)

2 3 4 5 (high B/M)

5-1

Panel A Loadings on HML

1 (small cap) -0.625 0.005 0.217 0.452 0.592 1.217 2 -0.485 0.121 0.322 0.656 0.736 1.221 3 -0.490 0.240 0.493 0.663 0.781 1.271 4 -0.588 0.302 0.467 0.645 0.568 1.157

5 (large cap) -0.368 0.126 0.193 0.504 0.702 1.071 5-1 0.257 0.121 -0.024 0.052 0.110

Panel B Loadings on ERET

1 (small cap) 1.080 1.060 0.894 0.893 1.021 -0.059 2 1.025 0.920 0.939 0.984 1.016 -0.010 3 0.971 0.933 0.878 0.996 0.909 -0.061 4 0.893 0.925 0.945 1.005 1.028 0.134

5 (large cap) 1.000 0.985 0.877 0.967 1.067 0.067 5-1 -0.187 -0.135 0.052 0.112 0.006

Panel C Loadings on SMB

1 (small cap) 1.722 1.581 1.338 1.281 1.375 -0.347 2 1.165 0.958 1.034 0.875 0.898 -0.267 3 0.796 0.784 0.651 0.724 0.835 0.039 4 0.496 0.401 0.434 0.452 0.487 -0.009

5 (large cap) -0.115 -0.002 0.007 0.027 0.018 0.133 5-1 -1.837 -1.583 -1.331 -1.255 -1.358 0.480

Note: The table reports loadings of twenty-five Fama and French (1996) portfolios on risk factors:

, 1 1 1 2 1 3 1 1HML MKT SMBpi t t t t tR α β β β η+ + + + += + + + + ,

where HML is the high-minus-low factor; ERET is the excess stock market return; and SMB is the small-minus-big

factor. The annual data span the period 1960 to 2006.

52

Table 7

Cross-Sectional Regressions with Fama and French 25 Portfolios

Constant ERET SMB HML IPOFDRΔ HML+ IPOFDR+Δ R2

Panel A IPOFDRΔ from First Difference

1 0.075 [1.659] <1.455>

-0.024 [-0.466] <-0.420>

0.036 [1.661] <1.656>

0.065** [3.161] <3.145>

0.834

2 0.072 [1.770] <1.240>

-0.024 [-0.501] <-0.378>

0.036 [1.648] <1.629>

0.126* [2.968] <2.263>

0.854

3 0.068 [1.523] <1.118>

-0.019 [-0.374] <-0.290>

0.036 [1.648] <1.632>

0.112 [2.302] <1.790>

0.016 [0.681] <0.578>

0.855

4 0.068 [1.523] <1.118>

-0.019 [-0.374] <-0.290>

0.036 [1.648] <1.632>

0.063** [3.085] <3.050>

0.076 [1.641] <1.264>

0.855

Panel B IPOFDRΔ from AR(1) Model

5 0.120* [2.925] <2.103>

-0.071 [-1.488] <-1.144>

0.037 [1.695] <1.678>

0.097* [2.823] <2.218>

0.847

6 0.105 [2.228] <1.723>

-0.055 [-1.027] <-0.828>

0.036 [1.687] <1.675>

0.079* [2.399] <2.010>

0.027 [1.299] <1.196>

0.848

7 0.105 [2.228] <1.723>

-0.055 [-1.027] <-0.828>

0.036 [1.687] <1.675>

0.064** [3.088] <3.058>

0.051 [1.631] <1.354>

0.848

Note: The table reports the Fama and MacBeth (1973) cross-sectional regression results. The annual data span the

1960 to 2006 period. ERET is the excess stock market return; HML and SMB are the value premium and the size

premium, respectively, of the Fama and French (1996) 3-factor model; IPOFDRΔ is the first difference of

IPOFDR; HML+ is the residual from the regression of HML on IPOFDRΔ , and IPOFDR +Δ is the residual from the

regression of IPOFDRΔ on HML. Fama and MacBeth t-statistics are reported in squared brackets and Shanken

(1992) corrected t-statistics are reported in angled brackets. Asterisks * or ** indicate significance at the 5% and 1%

levels, respectively.

53

Table 8

Forecasting One-Year-Ahead Dividend Growth

DP EP IPOFDR IPOFDR*DUM 2R

Panel A OLS Regressions

1 -0.836 (0.561)

0.045

2 -0.316 (0.187)

0.024

3 0.116** (0.033)

0.140

4 -1.238** (0.404)

0.134** (0.036)

0.237

5 -0.374* (0.170)

0.123** (0.034)

0.186

6 -1.314** (0.419)

0.139** (0.036)

-0.022 (0.043)

0.231

Panel B 2SLS Regressions

7 0.148** (0.038)

0.140

8 -1.105** (0.368)

0.222** (0.040)

0.213

9 -0.223 (0.152)

0.168** (0.039)

0.165

10 -1.217** (0.388)

0.218** (0.041)

-0.064 (0.047)

0.209

Note: The table reports the OLS estimation results of forecasting annual dividend growth. The annual data span the

1961 to 2006 period. DP is the dividend yield; EP is the earning-price ratio; IPOFDR is minus average IPO first-day

returns; and DUM is a dummy variable, which equals one for the years during which the number of IPOs is less than

200 and equals zero otherwise. White-corrected standard errors are reported in parentheses. Asterisks * or **

indicate significance at the 5% and 1% levels, respectively.

54

Table 9

Explaining Time-Series Variation in Investor Sentiment: 1962 to 2005

IV MV 2R CEFD -1.825*

(0.691) 6.088** (1.754)

0.081

TURN 5.692* (2.604)

-7.415 (8.239)

0.045

NIPO 6.717* (3.010)

-16.408 (9.173)

0.029

LNIPO 4.340* (1.631)

-1.059* (0.514)

0.124

IPOFDR -10.042** (2.435)

13.539** (3.906)

0.328

S -1.617 (0.836)

3.009 (2.912)

-0.018

PDND -8.818** (3.063)

14.521** (5.167)

0.150

SENT 52.413** (8.680)

-82.814** (25.069)

0.189

SENT⊥ 50.436** (7.431)

-52.991** (18.136)

0.195

Note: The table reports the OLS estimation results of regressing Baker and Wurgler’s (2006) measures of investor

sentiment on contemporaneous market variance (MV) and average idiosyncratic variance (IV) over the period 1962

to 2005. CEFD is the close-end fund discount; TURN is the NYSE share turnover; NIPO is the number of IPOs;

LNIPO is the log transformation of NIPO; IPOFDR is the IPO first-day return; S is the equity share in new issues;

PDND is dividend premium—the log difference of the average market-to-book equity ratio between dividend payers

and nonpayers; and SENT is the composite sentiment index. Baker and Wurgler (2006) also construct a second

index— SENT⊥ —by removing business-cycle variation from each of the six investor sentiment measures prior to

the principal components analysis. White-corrected standard errors are reported in parentheses. Asterisks * or **

indicate significance at the 5% and 1% levels, respectively.

55

Table 10

Investor Sentiment and One-Year Ahead Excess Market Returns: 1963 to 2006

Panel A Equity Share and Composite Investor Sentiment

S(-1) SENT(-1) SENT⊥ (-1) IPOFDR(-1) IPOFDR(-2) Wald Test 2R

1 -0.563* (0.269)

0.069

2 -0.026 (0.022)

0.003

3 -0.025 (0.022)

0.001

4 0.379** (0.119)

0.103

5 0.337** (0.119)

0.078

6 0.319* (0.136)

0.181 (0.144)

0.500** (0.138)

0.113

7 -0.480 (0.296)

0.310* (0.132)

0.151 (0.186)

0.462** (0.153)

0.169

8 0.040 (0.033)

0.315* (0.129)

0.394 (0.209)

0.709** (0.194)

0.119

9 0.054 (0.033)

0.330* (0.143)

0.467* (0.210)

0.797** (0.226)

0.134

Panel B Other Components of Investor Sentiment Index

PDND(-1) CEFD(-1) NIPO(-1) TURN(-1) IPOFDR(-1) IPOFDR(-2) Wald Test

2R

10 0.000 (0.002)

-0.021

11 0.002 (0.003)

-0.017

12 0.063 (0.923)

-0.024

13 0.035 (0.093)

-0.020

14 -0.004* (0.002)

0.608** (0.144)

0.273 (0.152)

0.881** (0.197)

0.199

15 -0.001 (0.003)

0.285* (0.136)

0.231 (0.152)

0.516** (0.131)

0.094

16 0.690 (0.956)

0.287* (0.134)

0.243 (0.141)

0.531** (0.134)

0.104

17 0.091 (0.074)

0.303* (0.142)

0.237 (0.153)

0.540** (0.127)

0.116

56

Note: The table reports the OLS estimation results of forecasting annual excess market returns using Baker and

Wurgler’s (2006) measures of investor sentiment. CEFD is the close-end fund discount; TURN is the NYSE share

turnover; NIPO is the number of IPOs; LNIPO is the log transformation of NIPO; IPOFDR is minus average IPO

first-day return; S is the equity share in new issues; PDND is dividend premium—the log difference of the average

market-to-book equity ratio between dividend payers and nonpayers; and SENT is the composite sentiment index.

Baker and Wurgler also construct an alternative index— SENT⊥ —by removing business-cycle variation from each

of the six investor sentiment measures prior to the principal components analysis. White-corrected standard errors

are reported in parentheses. Asterisks * or ** indicate significance at the 5% and 1% levels, respectively.

57

Table 11

Forecasting One-Year-Ahead Returns on Portfolios Sorted on Volatility

SENT(-1) IPOFDR(-1) IV(-1) MV(-1) ERET SMB IPODFRΔ 2RPanel A: Returns Difference between High and Low IV Stocks

1 -0.128** (0.021)

0.232

2 0.637** (0.167)

0.123

3 -11.694** (2.883)

23.421** (6.570)

0.146

Panel B: Returns Difference between High and Low IV Stocks: Controlling for ERET, SMB, and IPODFRΔ

4 0.271 (0.224)

0.665** (0.208)

-0.631* (0.256)

0.471

5 -0.044 (0.025)

0.037

6 0.193 (0.219)

0.003

7 -5.642* (2.293)

11.356* (5.575)

0.043

Note: The table reports in rows 1 to 3 the OLS estimation results of forecasting annual returns on the portfolio that is

long in stocks with high idiosyncratic volatility and short in stocks with low idiosyncratic volatility over the period

1963 to 2006. Row 4 reports the OLS estimation results of regressing the portfolio return on contemporaneous risk

factors. Rows 5 to 7 report the OLS estimation results of forecasting the residual from the regression reported in row

4. SENT is Baker and Wurgler’s (2006) investor sentiment index; IPOFDR is minus average IPO first-day returns;

IV is average idiosyncratic variance; MV is stock market variance; ERET is excess stock market return; SMB is the

return difference between small and big stocks; and IPOFDRΔ is the first difference of IPOFDR. White-corrected

standard errors are reported in parentheses. Asterisks * or ** indicate significance at the 5% and 1% levels,

respectively.